The UN Definition of War Crimes includes:
• making the civilian population or individual civilians, not taking a direct part in hostilities, the object of attack;
• launching an attack in the knowledge that such attack will cause incidental loss of civilian life, injury to civilians or damage to civilian objects which would be clearly excessive in relation to the concrete and direct military advantage anticipated;
• making non-defended localities and demilitarized zones the object of attack;
Hard to argue that the dropping of a Nuclear Weapon on a civilian target does not breach all three of these 'rules' .... yes it was a different time, yes the Japanese had done terrible things, however if you accept that the killing of women and children to theoretically prevent the loss of soldier's lives is an acceptable act? where do you draw the line? Is rape OK if it will stop the next village from fighting? is beheading of children OK to stop parents fighting? is bombing civilian targets ever acceptable?
Only one Country has ever used Nuclear Weapons and they did so at very the first opportunity they got .... did their action save soldiers lives, quite probably. Does that make this act of mass murder justifiable? probably not ....
So should the USA apologise for murdering 10's of 1000's of civilians .... well why not? They can couch the apology to say "what we did we deemed necessary"and yet still say "we're terribly sorry for the death and suffering we caused" .... no loss of face to anyone .... it's just a shame political arrogance prevents it ......